The club are currently known as Hull City AFC but Allam said over the summer that he wanted to rebrand the team as Hull Tigers.
But a range of supporters' groups who are opposed to the change have combined under the name City Till We Die and will be given the opportunity to put their case to Allam later this week.
Allam told the Hull Daily Mail in the summer: "Hull City is irrelevant. My dislike for the word 'City' is because it is common.
"I don't like being like everyone else, I want the club to be special. City is a lousy identity."
However, the City Till We Die group have released a statement which read: "City Till We Die campaigners will be urging Dr Allam to reconsider his decision to change Hull City's 109-year-old name, explaining that it is an important part of the local community, and that a rebrand to 'Hull Tigers' is not necessary to market the club more successfully.
"They will also be calling on the owner to engage in proper consultation with supporters."